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Quadratic_Equations/247790: Translate the problem into a pair of linear equations in two vaiables. Solve the equations using either elimination or substitution. State your answer for the specified variable. Andy has 14 coins made up of quarters and half-dollars, and their total value is $4.25. How many quarters does he have? 1 solutions Answer 180637 by solver91311(16868)   on 2009-12-09 11:57:43 (Show Source): You can put this solution on YOUR website! Let represent the number of quarters. Let represent the number of half-dollars. Then is the value of the quarters in cents and is the value of the half-dollars in cents. The total amount of money he has, expressed in cents, is 425. He has 14 coins: The total value is $4.25: Either of the elimination or substitution will work just fine to solve this system, but given the simplicity of the first equation, I would choose the substitution method. Let me know what you obtained for an answer. John

Linear-systems/247412: i am learning elimination using multiplication and i am really stuck i get everything i just dont get how you find the number that you have to multiply by this is the problem i need help on 3x+2y=-9 x-y=-13 i dont know how you figure out which number you multiply the equation by can you please help me 1 solutions Answer 180510 by solver91311(16868)   on 2009-12-08 18:53:31 (Show Source): You can put this solution on YOUR website! Every real number has a number called an additive inverse. The additive inverse is that number when added to the original number results in zero. The additive inverse of is because . The additive inverse of is . The additive inverse of is . The name of the method gives us a clue. The goal of the elimination method is to eliminate one of the variables. A variable can be eliminated only when the coefficient on that variable in one equation is the additive inverse of the coefficient on that same variable in the other equation. In your set, you have a 2 coefficient on in the first equation. What is the additive inverse of 2? The coefficient on in the second equation is -1. What would you have to multiply -1 by in order to make it the additive inverse of 2? The answer to that question is an answer to your question. It is just as correct as the other answer. There is another answer to your question because there is nothing sacred about which variable you eliminate. Either one works and leads you to the exact same solution set. If, instead of eliminating you wanted to eliminate , note that the coefficient on in the first equation is 3, so you have to change the second equation so that the coefficient on , currently 1, is the additive inverse of 3, namely -3. Note that this particular problem is very straightforward. You only need to find one multiplier. Later down the road you will run into situations where you will need to find two multipliers. Thus: Here, in order to eliminate , you need to multiply the first equation by 3 and the second equation by -7 (or -3 and 7 if you prefer -- doesn't matter in the end). And in order to eliminate you would multiply the first equation by 4 and the second equation by 5]. John

Graphs/247414: I have to solve the compound inequality. 5 < k - 2 < 11 1 solutions Answer 180500 by solver91311(16868)   on 2009-12-08 18:33:34 (Show Source): You can put this solution on YOUR website! Add 2 to all three parts of the inequality. John

percentage/247391: How do you turn percentages into parts on a circle or pie graph. 1 solutions Answer 180499 by solver91311(16868)   on 2009-12-08 18:32:53 (Show Source): You can put this solution on YOUR website! Change the percentage to a decimal fraction. Multiply 360 (the number of degrees in a circle) by the decimal fraction. The result is the angle measure of your pie slice. For example, 10% would be a 36 degree angle. 25% would be a 90 degree angle. 17.5% would be 360 times .175 = 63 degrees. John

Triangles/247396: can the lengths 0.5,0.7,0.3 make a proper triangle 1 solutions Answer 180496 by solver91311(16868)   on 2009-12-08 18:26:43 (Show Source): You can put this solution on YOUR website! You have three numbers, so you can make three different pairs of numbers. If all possible sums of two of the numbers are greater than the third number, then it is possible to make a triangle. For example, 0.5, 0.8, and 0.3 would NOT make a triangle. Because 0.5 + 0.3 = 0.8. That means you would have a straight line instead of a triangle. John

Parallelograms/247398: how would you find the variable of a parallelogram when there is two seperate variables but they are supposed to be equal to eachother? 1 solutions Answer 180493 by solver91311(16868)   on 2009-12-08 18:21:56 (Show Source): You can put this solution on YOUR website! Not enough information to answer this question. You need to describe your diagram in sufficient detail that someone can reproduce it without ambiguity. And the word is "separate" not "seperate" John

Expressions-with-variables/247400: A=B over C, solve for B 1 solutions Answer 180491 by solver91311(16868)   on 2009-12-08 18:18:46 (Show Source): You can put this solution on YOUR website! Multiply both sides by C John

Triangles/247392: the midpoint of the sides of a triangle are L(4,2),M(2,3)andN(5,4).What are the coordinates of the vertices of the triangle, please help. have a test tomm 1 solutions Answer 180490 by solver91311(16868)   on 2009-12-08 18:17:53 (Show Source): You can put this solution on YOUR website! A line segment that joins the midpoints of two sides of a triangle is parallel to the third side. So, using two of the given midpoints, you can calculate the slope of the segment that joins the mid-points using the slope formula. where and are the given mid-points. Then, using the slope you just calculated and the third midpoint, you can derive an equation of the line that contains the side of the triangle using the point-slope form of the equation of a line. where is the slope you just calculated and are the coordinates of the third mid-point. You need to perform the above procedure one more time using a different pair of midpoints. Now you have two equations that form a system of equations. The solution set of the system is the ordered pair representing one vertex of the triangle. Once you have one vertex, you can use the midpoint formulae to calculate the coordinates of the other two vertices. and You know and because they are givens, and you know and because they are the known vertex coordinates. John

Quadratic_Equations/247384: Determine whether the equation has two distinct real number solutions, one real numbers solution, or no real number solution. x^2 - 8x + 16 = 0 1 solutions Answer 180478 by solver91311(16868)   on 2009-12-08 17:59:57 (Show Source): You can put this solution on YOUR website! Compute the discriminant. The discriminant is the part of the quadratic formula , that is under the radical, namely Two real and unequal roots. If is a perfect square, then the roots are rational numbers, otherwise the roots are irrational. One real root with a multiplicity of two. That is to say that the trinomial is a perfect square and has two identical factors. No real solutions. Rather you have a conjugate pair of complex roots of the form where is the imaginary number defined by John

Exponents-negative-and-fractional/247368: 12y^2+54y-30 I have to factor the polynomial, if it can't be factored we have to write that it's prime 1 solutions Answer 180473 by solver91311(16868)   on 2009-12-08 17:54:31 (Show Source): You can put this solution on YOUR website! First take out a 6 Then notice that And And John

Square-cubic-other-roots/247361: What is the square root of 180 written in simplest radical form? 1 solutions Answer 180468 by solver91311(16868)   on 2009-12-08 17:30:31 (Show Source): You can put this solution on YOUR website! You need the prime factorization of 180 to start. 180 is divisible by 2, 180/2 = 90; one factor of 2 90 is divisible by 2, 90/2 = 45; two factors of 2 45 is not divisible by 2, but 4 + 5 = 9 is divisible by 3, so 45 is divisible by 3, 45/3 = 15, one factor of 3 15 is divisible by 3, 15/3 = 5, two factors of 3 5 is prime. So the prime factorization of 180 is Now you can write: But that can be written: John

Travel_Word_Problems/247360: A truck traveling at a constant rate of 45 miles per hour leaves Albany. one hour later a car traveling at a constant rate of 60 miles per hour also leaves albany traveling in the same direction on the same highway. how long will it take for the car to catch up to the truck, if both vehicles continue in the same direction on the highway? 1 solutions Answer 180463 by solver91311(16868)   on 2009-12-08 17:21:07 (Show Source): You can put this solution on YOUR website! Do this in your head. An hour after the first guy leaves going 45 miles per hour, he is 45 miles down the road. The other guy is going 15 miles per hour faster, so how long would it take someone going 15 miles per hour to go 45 miles? Think about it this way, what if the car stopped completely after an hour and the truck was only going 15 mph? Same as the car continuing at 45 and the truck going 60 -- the truck would catch up at a different place, but the amount of time would be the same. John

Word_Problems_With_Coins/247355: A collection of 20 coins made up of only nickels, dimes, and quarters has a total value of $3.35. If the dimes were nickels, the nickels were quarters and the quarters were dimes, the collection of coins would have a total value of $2.75. How many quarters are in the original collection? 1 solutions Answer 180461 by solver91311(16868)   on 2009-12-08 17:15:56 (Show Source): You can put this solution on YOUR website! Let represent the number of nickels. Let represent the number of dimes. Let represent the number of quarters. So altogether you have total coins. Then is the value of the nickels in cents. is the value of the dimes in cents, and is the value of the quarters in cents. All together, you have expressed in cents. But if you had quarters, you would have cents, and if you had nickels, you would have cents, and if you had dimes, you would have cents, and that would all add up to 275 cents, so: Now you have a system of three equations in three variables to solve. Since the problem only asks for the number of quarters, you really only need solve for , but I would solve for all three variables and plug the values back in to the original equations in order to check my work. John

Graphs/247352: Graph y=1 1 solutions Answer 180457 by solver91311(16868)   on 2009-12-08 17:06:09 (Show Source): You can put this solution on YOUR website! is another way of saying "the set of all ordered pairs " In other words, the set of ordered pairs where is replaced by all real numbers one at a time, and is always 1. If you still can't see it, pick a value, any value, for . Substitute that value into . Plot the point. Do it one more time with a different value for . Draw a line through both points. John

Rectangles/247341: a rectangular plot of ground containing 350 square ft is to be fenced. A)express teh amount of fence needed to enclose the rectangle on all sides as a function of the width,x 1 solutions Answer 180452 by solver91311(16868)   on 2009-12-08 16:59:51 (Show Source): You can put this solution on YOUR website! The area of a rectangle is given by So the length, in terms of the area and the width must be: The perimeter of a rectangle which is the distance around the rectangle and therefore the amount of fence required to enclose it is given by: Substituting for gives us a function for perimeter in terms of width for any given area For your 350 square foot area: John

Equations/247337: iam a 3 digit number less than 300 iam divisible by 2 and 5 but not 3 the sum of my digits is 7 what number am i. 1 solutions Answer 180446 by solver91311(16868)   on 2009-12-08 16:50:45 (Show Source): You can put this solution on YOUR website! Numbers that are divisible by 5 have a last digit of either 0 or 5. Numbers that are divisible by 2 are even numbers. Since any number that ends in 5 is not an even number, the number we are looking for must end in 0. Numbers that are divisible by 3 have a sum of digits that is divisible by 3. Since 7 is not divisible by 3, any number that qualifies by the fact that the sum of the digits is 7 also qualifies on non-divisibility by 3. Since this is a 3-digit number less than 300, the hundreds digit must be either 1 or 2. 7 minus 1 is 6, so one possibility is 160. 7 minus 2 is 5 so the other possibility is 250. John

Polynomials-and-rational-expressions/247328: Write the simplest polynomial function with the given zeros (-2, 2, 4) 1 solutions Answer 180443 by solver91311(16868)   on 2009-12-08 16:39:29 (Show Source): You can put this solution on YOUR website! If a number is a zero of a polynomial, then the binomial is a factor of the polynomial. The simplest polynomial function with the given zeros is the polynomial function with the three factors that correspond to the three given zeros. Since there are three zeros, the polynomial function must be of the third degree. John

Polygons/247321: what is the number of sides a polygon has if the sum of the degree measures of the interior angle is 180°? 1 solutions Answer 180441 by solver91311(16868)   on 2009-12-08 16:35:48 (Show Source): You can put this solution on YOUR website! The sum of the interior angles of an -sided polygon is given by the formula: So set the formula equal to your given sum and then solve for John

Proportions/247280: The number of kilograms W of water in a human body varies directly as the total body weight B. A person who weighs 75 kg contains 54 kg of water. a) Find an equation of variation. b) How many kilograms of water are in a person who weighs 95 kg? 1 solutions Answer 180437 by solver91311(16868)   on 2009-12-08 16:12:29 (Show Source): You can put this solution on YOUR website! If kilos of water vary directly as total weight, then But we know that So: Solve for Then substitute this value for into . Then you can determine either or if given the other just by substituting the known value. John

Functions/247216: find the domain of each of the following rational functions. 2.) f(x) = 5x+6 2x-6 Simplify completely (I don't understand this) 6.) -7xy^2 28x^2 16.) x-2 8x^2-32 How do you put the line between the two sets of numbers? 1 solutions Answer 180390 by solver91311(16868)   on 2009-12-08 12:36:03 (Show Source): You can put this solution on YOUR website! Like this: You write: f(x) = (5x+6)/(2x-6) [The parentheses are essential] I read that as The domain of a rational function is all real numbers EXCEPT any number that would make any denominator equal to 0. So what number or numbers would make ? ===================================== There is one factor of -1 in the numerator and none in the denominator, so the -1 stays put. There is one factor of 7 in the numerator and one factor of 7 in the denominator because 28 equals 7 times 4. So the 7 that is common to both numerator and denominator goes away, leaving you with a 4 in the denominator. There is one factor of in the numerator and two factors of in the denominator. The one factor that is common goes away and you are left with one factor of in the denominator. There are 2 factors of in the numerator and none in the denominator, so the 2 that are in the numerator stay put. In summary, you have a factor of -1 and two factors of , (which is to say, one factor of ) in the numerator. You have one factor of 4 and one factor of in the denominator. Hence: ================================== The two terms in the denominator expression have a factor of 8 in common, so: The binomial expression in the denominator is the difference of two squares. Use the difference of two squares factorization: Now you can see that the numerator and denominator have a factor of in common. Eliminate that factor from both numerator and denominator: John

Graphs/247206: I have already passed algebra but didn't pass the EOC and have forgotten alot of information. But anyway one of my questions is using substituion and elimination. x-11y=-123 11x-y=-33 i forget where and how to start. could you please help me?? 1 solutions Answer 180387 by solver91311(16868)   on 2009-12-08 12:13:48 (Show Source): You can put this solution on YOUR website! Substitution Method: Solve one of your equations for one of the variables in terms of the other, then substitute the expression for the chosen variable into the second equation. Thus: Equation 1: Equation 2: Add 11y to both sides of Equation 1: Substitute into Equation 2: Now just simplify and solve for . Once you have the value of , substitute that back into either equation and solve for . Elimination Method: Multiply one or both equations by some value that makes the coefficient on one of the variables equal to the additive inverse of that same variable's coefficient in the other equation. Then add the equations term-by-term. The coefficient of the chosen variable in the sum will be zero, eliminating (hence the name of the method) that variable and leaving you with a single equation in a single variable that can be solved by ordinary means. Thus: Equation 1: Equation 2: Multiply Equation 2 by -11: Equation 3: Add Equation 3 to Equation 1, term-by-term: Equation 4: Notice that the term has been eliminated. Now all you have to do is solve: Equation 4: And then substitute the calculated value for back into either of the original equations and solve the result for . Let me know what you come up with. John

Quadratic_Equations/247077: solve using the quadratic formula. 1 solutions Answer 180307 by solver91311(16868)   on 2009-12-07 22:53:34 (Show Source): You can put this solution on YOUR website! First put it into standard form. Now note that , , and Just plug in the numbers and do the arithmetic: John

Numbers_Word_Problems/246693: How many positive multiples of 7 that are less than 1000 have a units digit of 3? 1 solutions Answer 180306 by solver91311(16868)   on 2009-12-07 22:49:17 (Show Source): You can put this solution on YOUR website! 7 as an integer divisor has the interesting characteristic that all 10 possible digits appear in the units digit position of numbers evenly divisible by it. What that means is that the number three appears as the units digit in every 10th integer that is evenly divisible by 7. 7 times 142 is 994, so there are exactly 142 positive multiples of 7 less than 1000. One tenth of these, ignoring the decimal fraction, end in a units digit of 3. Answer: 14. John

Equations/247058: What measure of angle is swept by the minute hand during the duration of a class if the class starts at 2:16 P.M. and ends at 2:47 P.M.? 1 solutions Answer 180301 by solver91311(16868)   on 2009-12-07 22:14:35 (Show Source): You can put this solution on YOUR website! It takes 60 minutes for the hand to go around a 360 degree circle. 2:16 to 2:47 is 31 minutes. Just set up a proportion: You can just solve this by cross-multiplying the way it is, but it is easier arithmetic if you reduce first: John

Angles/247057: Find the measure of the complement of a 75 degree angle 1 solutions Answer 180300 by solver91311(16868)   on 2009-12-07 22:09:07 (Show Source): You can put this solution on YOUR website! Subtract 75 from 90 John

Linear_Equations_And_Systems_Word_Problems/247060: betty and nancy make bracelets and necklaces in their spare time. every week they have available 10,000 grams of metal and 20 hours between them to work. it takes 50 grams of metal to make a necklace and 200 grams to make a bracelet. each necklace takes 30 minutes to make and one in each bracelet. they can use 150 gems a week if the profit is $6.50 for each necklace, and $3 for each bracelet, how many of each should they make each week to maximize their profit 1 solutions Answer 180299 by solver91311(16868)   on 2009-12-07 22:08:07 (Show Source): You can put this solution on YOUR website! You left out a goodly chunk of the information required to solve this problem. Send me ALL of the data and I'll give you a quote for a complete solution complete with graphs and a full explanation. John

Polynomials-and-rational-expressions/246706: Write the terms of the trinomial 40-t-35t^2 in descending powers of the variable. Thank You in advance. 1 solutions Answer 180298 by solver91311(16868)   on 2009-12-07 22:04:37 (Show Source): You can put this solution on YOUR website! Just write the terms in the opposite order. The sign in front of a term goes with the term. No sign on the front term, + is understood. John

Linear-equations/247053: I am stuck with this problem. Write each equation in slope-intercept form. y – 3 = - 3(x - 6) Exercise 1 solutions Answer 180297 by solver91311(16868)   on 2009-12-07 21:57:24 (Show Source): You can put this solution on YOUR website! Distribute the -3 across the x - 6, then add 3 to both sides. John

Divisibility_and_Prime_Numbers/247050: is x^2 - x^35 prime? 1 solutions Answer 180296 by solver91311(16868)   on 2009-12-07 21:56:06 (Show Source): You can put this solution on YOUR website! Of course not. At the very least you have the factor so that: And if you are factoring over the reals: John

Equations/247047: HOW DO YOU FIND THE ANSWER OF X IF YOUR EQUATION IS 3(X+2)-18 1 solutions Answer 180295 by solver91311(16868)   on 2009-12-07 21:48:10 (Show Source): You can put this solution on YOUR website! Step 1, and this is very important. Learn how to type your questions without using all caps. All caps is the electronic equivalent of shouting and is therefore both rude and annoying. Step 2, if you want to solve an equation, you have to have an equation. Unfortunately, there is no equation in your question. You have an expression. The reason that I know it is not an equation is that there is no equals sign. Sorry, but you cannot "solve" an expression. John

Radicals/246712: Rationalize the denominator please 3√4/6 √2divided by 2√6-√2 1 solutions Answer 180293 by solver91311(16868)   on 2009-12-07 21:33:01 (Show Source): You can put this solution on YOUR website! Read my lesson on rationalizing the denominator: Paste this link into your browser: http://www.algebra.com/algebra/homework/Radicals/rationalizingdenominators1.lesson John